NEETPhysicsNuclear Physics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The density of nuclear matter is approximately constant for all nuclei. Reason (R): The strong nuclear force is a long-range force and does not show any saturation effect. In the light of the above statements, choose the most appropriate answer from the options given below:
Options
- ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- BBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- CAssertion (A) is true but Reason (R) is false.
- DAssertion (A) is false but Reason (R) is true.
Correct answer
C. Assertion (A) is true but Reason (R) is false.
Step-by-step solution
The radius of a nucleus is given by R = R₀ A^ 1/3 . The volume of the nucleus is V = 4 3 R^3 = 4 3 R₀^3 A . The mass of the nucleus is approximately mA , where m is the average mass of a nucleon. Nuclear density = Mass Volume = mA 4 3 R₀^3 A = 3m 4 R₀^3 . Since m and R₀ are constants, the nuclear density is independent of the mass number A . Thus, Assertion (A) is true. The strong nuclear force is a short-range force (acting effectively only over distances of a few femtometers) and exhibits a saturation effect, mea